1 Overview
This supplementary document complements the paper Distance vs. time. Articulatory and acoustic consequences of reduced vowel duration in Polish.
The following sections illustrate:
- The articulatory data normalisation procedure.
- Descriptive plots of the raw data.
- Code and plots of the linear regression models.
- Summaries of the models in 3.
- Extra analyses of F0 and F3.
Only relevant R code is shown in this document.
The full code can be inspected on the OSF repository at https://osf.io/hy7nt/?view_only=d06775a2cb1d4786a0442b0f15d73296, in the file code/analysis.Rmd.
2 Normalisation procedure
This is Figure 1 from the paper, which illustrates the normalisation procedure. See paper for details.
## The origin is x = 16.8107470216526, y = -50.1837719761868.
3 Descriptive statistics plots
3.1 Articulatory undershoot
Tongue contours from ultrasound tongue imaging of speaker PL01. Tongue tip on the right.
## The origin is x = 16.8107470216526, y = -50.1837719761868.
## The origin is x = 16.8107470216526, y = -50.1837719761868.
3.2 Duration
Figure 2 from the paper with boxplots and means of vowel duration depending on speech rate and stress.
3.3 Vowel space
3.3.1 Acoustic vowel space
3.3.2 Articulatory vowel space
3.3.3 Save
4 Inferential statistics
4.1 VIF (multicollinearity)
VIF values below 3 indicate absence of multicollinearity (Zuur, Ieno, and Elphick 2010). For all predictors, VIF < 3.
## Variables VIF
## 1 duration 2.169934
## 2 f1.z 1.379401
## 3 f2.z 1.208097
## 4 f0.z 1.122029
## 5 rate 1.639475
## 6 stress 1.4519034.2 Duration
4.3 F1
4.4 F2
4.5 Z1
4.6 Z2
4.7 Composite plot
5 Model summaries
5.1 Duration
| duration.log | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 3.77 | 3.63 – 3.91 | <0.001 |
| rate [normal] | 0.19 | 0.09 – 0.30 | <0.001 |
| rate [slow] | 0.45 | 0.31 – 0.59 | <0.001 |
| V11 | 0.14 | 0.02 – 0.27 | 0.023 |
| V12 | -0.01 | -0.16 – 0.14 | 0.913 |
| V13 | 0.00 | -0.16 – 0.17 | 0.968 |
| V14 | 0.00 | -0.12 – 0.13 | 0.955 |
| V15 | -0.22 | -0.39 – -0.06 | 0.008 |
| stress [stressed] | 0.23 | 0.18 – 0.28 | <0.001 |
| rate [normal] * V11 | -0.01 | -0.09 – 0.07 | 0.786 |
| rate [slow] * V11 | -0.04 | -0.12 – 0.03 | 0.268 |
| rate [normal] * V12 | -0.01 | -0.09 – 0.07 | 0.780 |
| rate [slow] * V12 | 0.00 | -0.08 – 0.08 | 0.960 |
| rate [normal] * V13 | 0.05 | -0.03 – 0.13 | 0.182 |
| rate [slow] * V13 | -0.02 | -0.10 – 0.06 | 0.576 |
| rate [normal] * V14 | -0.01 | -0.08 – 0.07 | 0.901 |
| rate [slow] * V14 | 0.02 | -0.06 – 0.10 | 0.593 |
| rate [normal] * V15 | -0.04 | -0.12 – 0.04 | 0.308 |
| rate [slow] * V15 | 0.01 | -0.07 – 0.08 | 0.899 |
|
rate [normal] * stress [stressed] |
0.15 | 0.10 – 0.20 | <0.001 |
|
rate [slow] * stress [stressed] |
0.18 | 0.13 – 0.23 | <0.001 |
| V11 * stress [stressed] | 0.12 | 0.04 – 0.20 | 0.003 |
| V12 * stress [stressed] | -0.05 | -0.13 – 0.03 | 0.215 |
| V13 * stress [stressed] | -0.07 | -0.15 – 0.00 | 0.065 |
| V14 * stress [stressed] | 0.03 | -0.05 – 0.11 | 0.473 |
| V15 * stress [stressed] | -0.01 | -0.09 – 0.07 | 0.841 |
|
(rate [normal] * V11) * stress [stressed] |
-0.03 | -0.14 – 0.09 | 0.655 |
|
(rate [slow] * V11) * stress [stressed] |
-0.06 | -0.17 – 0.06 | 0.331 |
|
(rate [normal] * V12) * stress [stressed] |
-0.04 | -0.15 – 0.07 | 0.465 |
|
(rate [slow] * V12) * stress [stressed] |
-0.04 | -0.16 – 0.07 | 0.455 |
|
(rate [normal] * V13) * stress [stressed] |
-0.07 | -0.18 – 0.04 | 0.209 |
|
(rate [slow] * V13) * stress [stressed] |
-0.08 | -0.19 – 0.03 | 0.173 |
|
(rate [normal] * V14) * stress [stressed] |
0.00 | -0.11 – 0.11 | 0.977 |
|
(rate [slow] * V14) * stress [stressed] |
0.03 | -0.08 – 0.15 | 0.555 |
|
(rate [normal] * V15) * stress [stressed] |
0.12 | 0.01 – 0.23 | 0.040 |
|
(rate [slow] * V15) * stress [stressed] |
0.11 | 0.00 – 0.23 | 0.046 |
| Random Effects | |||
| σ2 | 0.04 | ||
| τ00 frame | 0.02 | ||
| τ00 speaker | 0.04 | ||
| τ11 speaker.ratenormal | 0.03 | ||
| τ11 speaker.rateslow | 0.05 | ||
| τ11 speaker.stressstressed | 0.00 | ||
| ρ01 speaker.ratenormal | -0.81 | ||
| ρ01 speaker.rateslow | -0.78 | ||
| ρ01 speaker.stressstressed | -0.48 | ||
| N speaker | 10 | ||
| N frame | 12 | ||
| Observations | 1440 | ||
| Marginal R2 / Conditional R2 | 0.706 / NA | ||
5.2 F1
| f1.z | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | -0.59 | -0.78 – -0.41 | <0.001 |
| V11 | 0.38 | 0.04 – 0.72 | 0.029 |
| V12 | 0.08 | -0.29 – 0.46 | 0.660 |
| V13 | -0.29 | -0.69 – 0.12 | 0.163 |
| V14 | 0.31 | -0.02 – 0.64 | 0.064 |
| V15 | -0.49 | -0.90 – -0.08 | 0.020 |
| duration | 0.01 | 0.01 – 0.01 | <0.001 |
| stress [stressed] | 0.40 | 0.24 – 0.56 | <0.001 |
| V11 * duration | 0.02 | 0.01 – 0.02 | <0.001 |
| V12 * duration | -0.00 | -0.00 – 0.00 | 0.710 |
| V13 * duration | -0.01 | -0.01 – -0.01 | <0.001 |
| V14 * duration | -0.00 | -0.01 – 0.00 | 0.180 |
| V15 * duration | 0.00 | -0.00 – 0.01 | 0.476 |
| V11 * stress [stressed] | 0.41 | 0.06 – 0.76 | 0.022 |
| V12 * stress [stressed] | -0.22 | -0.54 – 0.09 | 0.165 |
| V13 * stress [stressed] | -0.25 | -0.55 – 0.05 | 0.100 |
| V14 * stress [stressed] | 0.16 | -0.15 – 0.47 | 0.307 |
| V15 * stress [stressed] | 0.18 | -0.13 – 0.50 | 0.246 |
|
duration * stress [stressed] |
-0.00 | -0.01 – -0.00 | 0.005 |
|
(V11 * duration) * stress [stressed] |
-0.01 | -0.01 – -0.00 | 0.024 |
|
(V12 * duration) * stress [stressed] |
0.01 | 0.00 – 0.01 | 0.007 |
|
(V13 * duration) * stress [stressed] |
0.00 | -0.00 – 0.01 | 0.608 |
|
(V14 * duration) * stress [stressed] |
0.00 | -0.00 – 0.01 | 0.692 |
|
(V15 * duration) * stress [stressed] |
-0.01 | -0.01 – -0.00 | 0.019 |
| Random Effects | |||
| σ2 | 0.17 | ||
| τ00 frame | 0.07 | ||
| τ00 speaker | 0.00 | ||
| τ11 speaker.stressstressed | 0.01 | ||
| ρ01 speaker | -1.00 | ||
| N speaker | 10 | ||
| N frame | 12 | ||
| Observations | 1440 | ||
| Marginal R2 / Conditional R2 | 0.837 / NA | ||
5.3 F2
| f2.z | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | -0.06 | -0.24 – 0.13 | 0.550 |
| V11 | -0.38 | -0.69 – -0.07 | 0.015 |
| V12 | 0.28 | -0.08 – 0.63 | 0.132 |
| V13 | 1.17 | 0.77 – 1.57 | <0.001 |
| V14 | -0.52 | -0.82 – -0.22 | 0.001 |
| V15 | -0.67 | -1.08 – -0.27 | 0.001 |
| duration | 0.00 | -0.00 – 0.00 | 0.283 |
| stress [stressed] | 0.05 | -0.05 – 0.15 | 0.332 |
| V11 * duration | 0.00 | -0.00 – 0.00 | 0.426 |
| V12 * duration | 0.00 | -0.00 – 0.01 | 0.067 |
| V13 * duration | 0.01 | 0.00 – 0.01 | <0.001 |
| V14 * duration | -0.01 | -0.01 – -0.00 | <0.001 |
| V15 * duration | -0.01 | -0.01 – -0.00 | 0.002 |
| V11 * stress [stressed] | 0.04 | -0.21 – 0.29 | 0.765 |
| V12 * stress [stressed] | -0.02 | -0.25 – 0.20 | 0.843 |
| V13 * stress [stressed] | 0.29 | 0.08 – 0.51 | 0.008 |
| V14 * stress [stressed] | -0.12 | -0.34 – 0.10 | 0.269 |
| V15 * stress [stressed] | -0.26 | -0.48 – -0.03 | 0.025 |
|
duration * stress [stressed] |
-0.00 | -0.00 – 0.00 | 0.600 |
|
(V11 * duration) * stress [stressed] |
-0.00 | -0.00 – 0.00 | 0.630 |
|
(V12 * duration) * stress [stressed] |
0.00 | -0.00 – 0.00 | 0.858 |
|
(V13 * duration) * stress [stressed] |
-0.00 | -0.01 – 0.00 | 0.155 |
|
(V14 * duration) * stress [stressed] |
0.00 | -0.00 – 0.00 | 0.382 |
|
(V15 * duration) * stress [stressed] |
0.00 | -0.00 – 0.01 | 0.566 |
| Random Effects | |||
| σ2 | 0.09 | ||
| τ00 frame | 0.08 | ||
| τ00 speaker | 0.00 | ||
| τ11 speaker.stressstressed | 0.00 | ||
| ρ01 speaker | |||
| N speaker | 10 | ||
| N frame | 12 | ||
| Observations | 1440 | ||
| Marginal R2 / Conditional R2 | 0.908 / NA | ||
5.4 Z1
| z1 | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | -0.27 | -0.41 – -0.13 | <0.001 |
| V11 | 0.17 | -0.09 – 0.43 | 0.211 |
| V12 | -0.16 | -0.44 – 0.12 | 0.256 |
| V13 | -0.55 | -0.85 – -0.26 | <0.001 |
| V14 | 0.25 | 0.00 – 0.51 | 0.048 |
| V15 | 0.12 | -0.19 – 0.42 | 0.453 |
| duration | 0.00 | 0.00 – 0.01 | <0.001 |
| stress [stressed] | -0.02 | -0.15 – 0.11 | 0.801 |
| V11 * duration | 0.01 | 0.00 – 0.01 | <0.001 |
| V12 * duration | -0.00 | -0.00 – 0.00 | 0.859 |
| V13 * duration | -0.01 | -0.01 – -0.00 | 0.001 |
| V14 * duration | 0.01 | 0.00 – 0.01 | 0.002 |
| V15 * duration | -0.00 | -0.01 – 0.00 | 0.277 |
| V11 * stress [stressed] | -0.06 | -0.35 – 0.23 | 0.697 |
| V12 * stress [stressed] | 0.07 | -0.19 – 0.33 | 0.591 |
| V13 * stress [stressed] | -0.09 | -0.34 – 0.16 | 0.490 |
| V14 * stress [stressed] | 0.03 | -0.22 – 0.29 | 0.807 |
| V15 * stress [stressed] | 0.04 | -0.21 – 0.30 | 0.737 |
|
duration * stress [stressed] |
-0.00 | -0.00 – 0.00 | 0.619 |
|
(V11 * duration) * stress [stressed] |
-0.00 | -0.00 – 0.00 | 0.722 |
|
(V12 * duration) * stress [stressed] |
0.00 | -0.00 – 0.00 | 0.952 |
|
(V13 * duration) * stress [stressed] |
0.00 | -0.00 – 0.00 | 0.544 |
|
(V14 * duration) * stress [stressed] |
0.00 | -0.00 – 0.00 | 0.891 |
|
(V15 * duration) * stress [stressed] |
-0.00 | -0.01 – 0.00 | 0.591 |
| Random Effects | |||
| σ2 | 0.12 | ||
| τ00 frame | 0.03 | ||
| τ00 speaker | 0.00 | ||
| τ11 speaker.stressstressed | 0.01 | ||
| ρ01 speaker | -1.00 | ||
| N speaker | 10 | ||
| N frame | 12 | ||
| Observations | 1440 | ||
| Marginal R2 / Conditional R2 | 0.734 / NA | ||
5.5 Z2
| z2 | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.13 | -0.11 – 0.37 | 0.298 |
| V11 | -0.27 | -0.66 – 0.12 | 0.182 |
| V12 | 0.33 | -0.14 – 0.79 | 0.169 |
| V13 | 1.09 | 0.57 – 1.62 | <0.001 |
| V14 | -0.53 | -0.92 – -0.15 | 0.007 |
| V15 | -0.59 | -1.12 – -0.06 | 0.030 |
| duration | -0.00 | -0.00 – -0.00 | 0.004 |
| stress [stressed] | -0.04 | -0.15 – 0.06 | 0.406 |
| V11 * duration | -0.00 | -0.00 – 0.00 | 0.650 |
| V12 * duration | 0.00 | -0.00 – 0.00 | 0.607 |
| V13 * duration | 0.00 | 0.00 – 0.01 | 0.002 |
| V14 * duration | -0.00 | -0.01 – -0.00 | 0.005 |
| V15 * duration | -0.01 | -0.01 – -0.00 | 0.007 |
| V11 * stress [stressed] | 0.09 | -0.17 – 0.35 | 0.487 |
| V12 * stress [stressed] | -0.09 | -0.32 – 0.14 | 0.466 |
| V13 * stress [stressed] | 0.02 | -0.20 – 0.24 | 0.852 |
| V14 * stress [stressed] | 0.09 | -0.14 – 0.31 | 0.457 |
| V15 * stress [stressed] | -0.19 | -0.42 – 0.04 | 0.104 |
|
duration * stress [stressed] |
0.00 | -0.00 – 0.00 | 0.270 |
|
(V11 * duration) * stress [stressed] |
-0.00 | -0.01 – 0.00 | 0.326 |
|
(V12 * duration) * stress [stressed] |
0.00 | -0.00 – 0.00 | 0.779 |
|
(V13 * duration) * stress [stressed] |
0.00 | -0.00 – 0.00 | 0.658 |
|
(V14 * duration) * stress [stressed] |
-0.00 | -0.01 – 0.00 | 0.312 |
|
(V15 * duration) * stress [stressed] |
0.00 | -0.00 – 0.01 | 0.114 |
| Random Effects | |||
| σ2 | 0.09 | ||
| τ00 frame | 0.15 | ||
| τ00 speaker | 0.00 | ||
| τ11 speaker.stressstressed | 0.00 | ||
| ρ01 speaker | |||
| N speaker | 10 | ||
| N frame | 12 | ||
| Observations | 1440 | ||
| Marginal R2 / Conditional R2 | 0.874 / NA | ||
6 Further exploratory analyses
6.1 F0
## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 4 rows containing missing values (geom_point).| f0.z | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | -0.93 | -1.30 – -0.55 | <0.001 |
| V11 | 0.30 | -0.18 – 0.77 | 0.217 |
| V12 | -0.21 | -0.67 – 0.24 | 0.361 |
| V13 | 0.07 | -0.37 – 0.51 | 0.747 |
| V14 | -0.04 | -0.48 – 0.40 | 0.853 |
| V15 | 0.13 | -0.35 – 0.60 | 0.595 |
| duration | 0.01 | 0.01 – 0.02 | <0.001 |
| stress [stressed] | 0.81 | 0.11 – 1.51 | 0.023 |
| V11 * duration | -0.01 | -0.02 – -0.00 | 0.005 |
| V12 * duration | 0.00 | -0.01 – 0.01 | 0.802 |
| V13 * duration | -0.00 | -0.01 – 0.00 | 0.591 |
| V14 * duration | -0.00 | -0.01 – 0.01 | 0.639 |
| V15 * duration | 0.01 | 0.00 – 0.02 | 0.013 |
| V11 * stress [stressed] | -0.28 | -0.91 – 0.35 | 0.379 |
| V12 * stress [stressed] | 0.42 | -0.14 – 0.98 | 0.142 |
| V13 * stress [stressed] | -0.28 | -0.81 – 0.26 | 0.311 |
| V14 * stress [stressed] | 0.01 | -0.54 – 0.56 | 0.966 |
| V15 * stress [stressed] | 0.31 | -0.24 – 0.87 | 0.268 |
|
duration * stress [stressed] |
-0.01 | -0.01 – -0.00 | <0.001 |
|
(V11 * duration) * stress [stressed] |
0.01 | -0.00 – 0.01 | 0.218 |
|
(V12 * duration) * stress [stressed] |
-0.01 | -0.02 – 0.00 | 0.091 |
|
(V13 * duration) * stress [stressed] |
0.01 | -0.00 – 0.01 | 0.190 |
|
(V14 * duration) * stress [stressed] |
0.00 | -0.01 – 0.01 | 0.938 |
|
(V15 * duration) * stress [stressed] |
-0.01 | -0.02 – 0.00 | 0.194 |
| Random Effects | |||
| σ2 | 0.54 | ||
| τ00 frame | 0.03 | ||
| τ00 speaker | 0.24 | ||
| τ11 speaker.stressstressed | 1.11 | ||
| ρ01 speaker | -1.00 | ||
| N speaker | 10 | ||
| N frame | 12 | ||
| Observations | 1436 | ||
| Marginal R2 / Conditional R2 | 0.257 / NA | ||
6.2 F3
## `geom_smooth()` using formula 'y ~ x'
7 Session info
## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.0.3 (2020-10-10)
## os macOS Big Sur 10.16
## system x86_64, darwin17.0
## ui X11
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Europe/Berlin
## date 2021-03-31
##
## ─ Packages ───────────────────────────────────────────────────────────────────
## ! package * version date lib
## P abind 1.4-5 2016-07-21 [?]
## P assertthat 0.2.1 2019-03-21 [?]
## P backports 1.2.1 2020-12-09 [?]
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## P crayon 1.4.1 2021-02-08 [?]
## P curl 4.3 2019-12-02 [?]
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## P evaluate 0.14 2019-05-28 [?]
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## P httr 1.4.2 2020-07-20 [?]
## P insight 0.13.1 2021-02-22 [?]
## P jsonlite 1.7.2 2020-12-09 [?]
## P knitr 1.31 2021-01-27 [?]
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## P magrittr 2.0.1 2020-11-17 [?]
## P MASS 7.3-53.1 2021-02-12 [?]
## P Matrix * 1.3-2 2021-01-06 [?]
## P memoise 2.0.0 2021-01-26 [?]
## P mgcv 1.8-34 2021-02-16 [?]
## P minqa 1.2.4 2014-10-09 [?]
## P mitools 2.4 2019-04-26 [?]
## P modelr 0.1.8 2020-05-19 [?]
## P munsell 0.5.0 2018-06-12 [?]
## P mvtnorm 1.1-1 2020-06-09 [?]
## P nlme 3.1-152 2021-02-04 [?]
## P nloptr 1.2.2.2 2020-07-02 [?]
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## P numDeriv 2016.8-1.1 2019-06-06 [?]
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## P pkgconfig 2.0.3 2019-09-22 [?]
## P pkgload 1.2.0 2021-02-23 [?]
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## P readr * 1.4.0 2020-10-05 [?]
## P readxl 1.3.1 2019-03-13 [?]
## P remotes 2.2.0 2020-07-21 [?]
## P reprex 1.0.0 2021-01-27 [?]
## P rio 0.5.26 2021-03-01 [?]
## P rlang 0.4.10 2020-12-30 [?]
## P rmarkdown 2.7 2021-02-19 [?]
## P rmdformats 1.0.1 2021-01-13 [?]
## P rprojroot 2.0.2 2020-11-15 [?]
## P rstatix 0.7.0 2021-02-13 [?]
## P rstudioapi 0.13 2020-11-12 [?]
## P rticulate * 1.6.0 2021-03-18 [?]
## P rvest 1.0.0 2021-03-09 [?]
## P scales 1.1.1 2020-05-11 [?]
## P sessioninfo 1.1.1 2018-11-05 [?]
## P sjlabelled 1.1.7 2020-09-24 [?]
## P sjmisc 2.8.6 2021-01-07 [?]
## P sjPlot * 2.8.7 2021-01-10 [?]
## P sjstats 0.18.1 2021-01-09 [?]
## P sp * 1.4-5 2021-01-10 [?]
## P statmod 1.4.35 2020-10-19 [?]
## P stringi 1.5.3 2020-09-09 [?]
## P stringr * 1.4.0 2019-02-10 [?]
## P survey 4.0 2020-04-03 [?]
## P survival 3.2-10 2021-03-16 [?]
## P testthat 3.0.2 2021-02-14 [?]
## P tibble * 3.1.0 2021-02-25 [?]
## P tidyr * 1.1.3 2021-03-03 [?]
## P tidyselect 1.1.0 2020-05-11 [?]
## P tidyverse * 1.3.0 2019-11-21 [?]
## P usdm * 1.1-18 2017-06-25 [?]
## P usethis 2.0.1 2021-02-10 [?]
## P utf8 1.2.1 2021-03-12 [?]
## P vctrs 0.3.6 2020-12-17 [?]
## P withr 2.4.1 2021-01-26 [?]
## P xfun 0.22 2021-03-11 [?]
## P xml2 1.3.2 2020-04-23 [?]
## P xtable 1.8-4 2019-04-21 [?]
## P yaml 2.2.1 2020-02-01 [?]
## P zip 2.1.1 2020-08-27 [?]
## source
## CRAN (R 4.0.2)
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## Github (stefanocoretta/rticulate@7e8ec81)
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##
## [1] /Users/ste/repos/polish-reduction/renv/library/R-4.0/x86_64-apple-darwin17.0
## [2] /private/var/folders/yj/b5zvw9lj2zg6tp920wyg14y80000gn/T/RtmpWsGWyS/renv-system-library
## [3] /Library/Frameworks/R.framework/Versions/4.0/Resources/site-library
## [4] /Library/Frameworks/R.framework/Versions/4.0/Resources/library
##
## P ── Loaded and on-disk path mismatch.
Zuur, Alain F., Elena N. Ieno, and Chris S. Elphick. 2010. “A Protocol for Data Exploration to Avoid Common Statistical Problems.” Methods in Ecology and Evolution 1 (1): 3–14. https://doi.org/10.1111/j.2041-210X.2009.00001.x.